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Some analytical considerations


Characterized as a ‘zoologist by training, an epistemologist by vocation, and a logician by method,’ Piaget is best known for his contributions to developmental psychology. He regarded himself as an interdisplinary thinker; perhaps the identification ‘genetic epistemologist’ best described his orientation. Epistemology is the branch of science concerned with the methods, limits, and validity of knowledge. The term genetic is used in the sense of genesis or development; indeed, Piaget did not study the genes of his subjects, and the idea of genetic influences on the acquisition of knowledge applies only in a very broad sense. In regard to the nature-nurture controversy, Piaget was neither a maturationalist nor an environmentalist, but is better characterized as an ‘interactionist’ or ‘constructionist’. He came up with four stages of cognitive development.

• The sensorimotor
• Preoperational
• Concrete operational
• Formal operational

Each of Piaget’s four stages represent a stage in development of intelligence [hence Sensorimotor intelligence, preoperational intelligence, concrete operational intelligence, and formal operational intelligence] and is a way of summarizing the various schemas a child has at a particular time.

The ages given are approximate, because children move through the stages at different rates due to differences in both the environment and their biological maturation. Children also pass through transitional periods, in which their thinking is a mixture of two stages. The concept of developmental ‘stage’ is often taken to mean that development is discontinuous. But for Piaget, development is a gradual and continuous process of change although later stages build on earlier ones [which is why sequence is invariant].

The sensorimotor stage

This is the period during infancy. Development at this stage is based on information obtained from the senses [sensori] and from the actions or body movements [motor] on the part of the infant. Infants learn about the world primarily through the senses and by doing. The infant’s greatest developmental achievement is the realization that objects in the environment exist whether perceived or not. This basic understanding is called object permanence.
Infants begin to recognize that hidden objects do not cease to exist. A second major achievement or accomplishment at this stage is the beginning of logical goal-directed actions. For example, if a child wants to get what is in a covered container he or she may build a scheme as follows:

• Get the lid off
• Turn the container upside down
• Shake if the item falls
• Watch the item fall on the floor
The child may also reverse this action by refilling the container. But a very young child will struggle to get the contents out. So the child moves from reflex action to goal directed activity.

The preoperational stage

This stage takes place during early childhood from 2-7 years. This period is also denoted the preschool period. This is a stage before the child masters logical and mental operations. These are actions carried out by thinking them through instead of literally performing them. Because, the child has not mastered these operations, hence the reference preoperational. The fact however is that the child is moving towards mastery. According to Piaget, the first step from action to thinking is the internalization of actions. This means, performing an action mentally not physically.

The first type of thinking that is separate from action, involves making an action scheme symbolic. So the ability to form and use the symbolic – words, gestures, signs and images- is a major accomplishment at this stage. This accomplishment moves children closer to mastering mental operations. This ability to work with symbols such as using the word [bicycle] or a [picture] of a bicycle that is not actually present is called the sembiotic formation. During the preoperational stage there is rapid development of the very important symbolic system---language.

As the child moves through this stage, the developing ability to think about objects in symbolic form remains limited to thinking in one direction only or using one-way logic. It is very difficult for the child to think backwards---reverse thinking.
According to Piaget, preoperational children are egocentric. This is the tendency to see the world and the experiences of others from one’s own perspective only. The child cannot appreciate that other people might see things differently. Egocentrism does not imply that the child is selfish however. Rather it simply means children often assume that everyone else shares their feelings, reactions, and perspectives. Furthermore egocentrism is also evident in the child’s language. Children happily talk of what they are doing even though no one is listening. This happens when a child is alone or with a group of other children. In a group, each child talks enthusiastically without real interaction or conversation. Piaget calls this the collective monologue. Other weaknesses include transductive reasoning, animism and artificialism.

Transductive reasoning involves drawing an inference about the relationship between two things based on a single shared attribute. An example being cats must be dogs because they all have four legs. Animism refers to the belief that all inanimate objects are alive. Artificialism is the belief that natural features have been designed and constructed by people, for example, the question ‘why is the sky blue?’ might produce an answer from a preoperational child that ‘somebody painted it’.

Preoperational children also lack the abilities to apply:

• Conservation
• Classification
• Seriation

The concrete operational stage

This stage takes place during the later primary to middle school years from 7-11 years. The basic characteristics of this stage are:

• The recognition of the logical system of the physical world.
• The realization that elements can be changed or transformed but still conserve many of their original characteristics.
• The understanding that these changes can be reversed.
• Operational thought is reversible----logical operations can be reversed by canceling an operation.
• Operational thought is associative----thought is not limited to one avenue.

In this stage mental tasks are tied to concrete objects and situations.

According to Piaget, a student’s ability to solve conservation problems depends on the understanding of basic aspects of reasoning such as identity, compensation and reversibility.

Conservation is the understanding that any quantity [e.g. number, liquid quantity, length and substance], remains the same despite physical changes in the arrangements of objects. Piaget believed that preoperational children cannot conserve because their thinking is dominated by the perceptual nature of objects [appearance].

Elements of conservation include:

• Identity
• Compensation
• Reversibility


It is the principle that quantity or mass in objects remains the same over time.
For instance a round mould when reshaped into a sausage still retains the same volume and characteristics regardless of the change. With complete mastery of identity, the student knows that if nothing is added or taken away the material remains the same.


It is the principle that changes in one dimension can be offset by changes in another as in changes in matter form from liquid to gas, solid to fluid. With an understanding of compensation the student knows that an apparent change in one dimension can be compensated for by a change in another dimension.


It is the ability to think things through a series of steps and return to the starting point. The child is able to comprehend that if 1 + 3 = 4 then 4 – 3 = 1-----in other words he or she can reverse mathematical or any other computations. With an understanding of reversibility the student can actually cancel out the change that has been made. A grasp of reversibility means that the student has mastered two-way thinking.


Involves focusing on only a single perceptual quality at a time. In a test of conservation a child is presented with two tubes of the same volume but of different dimensions-----the other narrow but high and the other squat but wide.
Queried which has more liquid when liquid of the same volume is poured
into both of the two dimensionally different tubes:

A child in the preoperational stage would deduce the narrow one has more liquid even though both have the same volume of liquid while a child in the concrete operational stage would be able to understand that the two have the same volume and hence hold the same amount of liquid.

This would be the case even when the situation was reversed. Preoperational children lack the ability to decentre. As documented in the example above they only focus on the perceptual nature in this case length and height of the object.

Apart from conservation other important operations achieved at this stage include:

• Classification
• Seriation


Classification is the grouping of objects into categories. Classification depends on the student’s abilities to form simple characteristics of objects in a set and group the objects according to their characteristics. Given a mixture of fruits---mangoes, bananas, apples—the child is able to group them into sets of [M], [B], and [A].


Seriation is the process of making an orderly arrangement from large to small or vice versa. The preoperational child has difficulty arranging objects on the basis of a particular dimension e.g. color, length and shape. With abilities to handle operations like conservation, classification and seriation; the student has finally developed a complete and very logical system of thinking. This system of thinking is, however, tied to physical reality. The concrete operational child is not yet able to reason about hypothetical, abstract problems that involve the coordination of many factors at once.

The formal operational stage

Piaget’s formal operations include, among others, the use of propositional thinking, combinatorial analysis, proportional reasoning, probabilistic reasoning, correlational reasoning, and abstract reasoning. The concept formal implies that what matters is form and logic rather than content. With the progression through these stages, mental operations become increasingly more abstract, more complex, more logical, and the boundaries of the mental structures become more permeable and thus, provide thought processes with greater flexibility.

This stage takes place during junior and senior secondary school from 11-15 years and older yet not all people acquire this level of abstract/logical thinking. This stage deals with mental tasks involving abstract thinking and coordination of a number of variables. All the earlier operations and abilities continue and are integrated. The focus of thinking shifts from what is to what might be. Situations do not have to be experienced to be imagined. A student at this stage attains hypothetical deductive reasoning as a major achievement at this stage.

This is a formal operations problem-solving strategy in which an individual begins by identifying all the factors that might affect a problem and then deduces and systematically evaluates specific solutions, for example moving from general to specific.

Adolescent thought is thus more abstract than child thought. Adolescents are no longer limited to actual, concrete experiences as anchors for thought. They can conjure up make-believe situations, events that are strictly hypothetical possibilities or purely abstract propositions, and try to reason logically about them. The abstract quality of the adolescent’s thought at the formal operational level is evident in the adolescent’s verbal problem-solving ability. While the concrete operational thinker would need to see the concrete elements A, B, and C to be able to make the logical inference that if A= B and B= C then A= C, the formal operational thinker can solve this problem merely through verbal presentation. This reflects a reasoning ability connoted Transitive inference: the ability to solve problems verbally and logically.

Furthermore children who function at the concrete operational stage cannot solve the transitive inference problem if it is placed on a purely verbal and hypothetical plane e.g. ‘John is taller than Mary, Mary is taller than Jane. Who is the tallest?’ They are unable to consider all the possible combinations in relation to the whole problem [Harris and Butterworth, 2002].

Another indication of the abstract quality of the adolescent’s thought is his or her increased tendency to think about thought itself. One adolescent commented, ‘I began thinking about why I was thinking what I was, then I began thinking about why I was thinking about why I was thinking about why I was’. If that sounds abstract, it is, and it characterizes the adolescent’s enhanced focus on thought and its abstract qualities. Accompanying the abstract nature of formal operational thought in adolescence is thought full of idealism and possibilities. While children frequently think in concrete ways, or in terms of what is real and limited, adolescents begin to engage in extended speculation about ideal characteristics- qualities they desire in themselves and in others.

Such thoughts often lead adolescents to compare themselves and others in regard to such ideal standards. And during adolescence, the thoughts of individuals are often fantasy flights into future possibilities. It is not unusual for the adolescent to become impatient with these newfound ideal standards and become perplexed over which of many ideal standards to adopt. It is sometimes said that the adolescent’s thought is more like a scientist’s than a child’s. This implies that the adolescent often entertains many possibilities and tests many solutions in a planned way when having to solve a problem. This kind of problem solving as already alluded to has been called hypothetical deductive reasoning. Basically this means that in solving a problem, an individual develops hypotheses or hunches about what will be a correct solution to the problem, and then in a planned manner tests one or more of the hypotheses, discarding the ones that do not work.

Adolescents can thus think about possibilities, think through hypothesis, think ahead, think about thought and engage in perspective thinking. Perspective thinking relates to the awareness that different people have different thoughts about the same situation. While children are egocentric adolescents are socio-centric. According to Muuss [1996] adolescents not only think beyond the present but analytically reflect about their own thinking. Piaget calls this type of reasoning ‘second-degree thinking’ which involves operations that produce ‘thinking about thinking’, ‘statements about statements’, or more significantly ‘operations on operations’.

The other distinctive property of formal thought is the reversal of direction between reality and possibility. A type of thinking which proceeds from what is possible to what is empirically real [Inhelder and Piaget, 1958].
Combinational systems of operations defined as the matrix of all possible combinations of all possible values of all possible variables inherent in the problem also constitutes formal operations. Combinational analysis can be exemplified by an experiment requesting to determine which combination of five chemicals produces a yellowish-brown liquid and which returns the liquid to its original colorless state.

Yet another cognitive ability attained at this stage is Propositional analysis entailing the ability to follow and understand logical deductions in the light of two premises---one specific, the other general---- and a conclusion.

E.g. :
A] All human beings are mortal.
John is a human being.
Therefore John is mortal.

B] All planets orbit the sun.
The earth is a planet.
Therefore the earth orbits the sun.


According to David Elkind [1967, 1976, 1978] two important aspects of thinking about the self and others that develop in adolescence are egocentrism and perspective taking. David Elkind believes two types of thinking represent the emergence of egocentrism in adolescents. These are the imaginary audience and the personal fable. Imaginary audience is the belief that others are as pre-occupied with the adolescent’s behavior as he or she is. Attention-seeking behavior, so common in early adolescence, may reflect this interest in an, imaginary audience, that is the desire to be noticed, visible, and on stage.

Particularly during early adolescence, individuals see themselves as constantly on stage, believing they are the main actors and all others are the audience. The construction personal fable on the other hand refers to the adolescent’s sense of personal uniqueness and indestructibility. Their sense of personal uniqueness makes them feel that no one can understand how they really feel that they are special. Another aspect of the personal fable involves the belief that one is indestructible. This results in feelings of invulnerability or insusceptibility and therefore risk-taking behaviors such as alcoholism/drug and substance abuse as well as sexual promiscuity.


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